WASHINGTON — Despite political tensions between the United States and Russia, the two nations’ militaries are cooperating closely — particularly in Syria, President Trump and President Vladimir V. Putin said on Monday.

But their record of collaboration — or at least efforts to avoid conflict — in the war in Syria is far more mixed.

After his meeting with Mr. Trump in Helsinki, Finland, Mr. Putin said in a joint news conference that military cooperation in Syria could be “the first showcase example of the successful joint work” between the two Cold War rivals. He noted that communication channels between the two countries’ militaries have been able to “avoid dangerous incidents and unintentional collisions in the air and in the ground.”

“Our militaries do get along very well, and they do coordinate in Syria and other places,” Mr. Trump chimed in. “Our militaries actually have gotten along probably better than our political leaders, for years.”

Yet it is not clear what room there is for close ties in Syria — other than preventing clashes on the ground or crashes in the sky — given Russia’s backing of the government of President Bashar al-Assad of Syria and the United States’ support for rebel factions.

Russian mercenaries have battled American commandos and their Syrian Kurdish allies. Russian and American warplanes have nearly collided.

Here are five areas where the American and Russian militaries have crossed paths in Syria over the last year.

The generals

The two nations’ top military officers, Gen. Joseph F. Dunford Jr., the chairman of the Joint Chiefs of Staff, and Gen. Valery V. Gerasimov, Russia’s chief of the general staff, meet occasionally. They talk more frequently — mainly to help prevent the two militaries from jousting in increasingly close quarters in Syria.

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Gen. Valery V. Gerasimov, left, Russia’s chief of the general staff, across from Gen. Joseph F. Dunford Jr., the chairman of the Joint Chiefs of Staff, at meeting in Helsinki, Finland, last month. The two meet occasionally and talk more frequently to head off potential conflicts between their two militaries in Syria.CreditLehtikuva/Reuters

The generals met on June 8 in Helsinki to discuss Syria, security in Europe and overall United States-Russia military relations, General Dunford’s spokesman said. It was their first face-to-face meeting since March 6, 2017, in Antalya, Turkey. They also met on Feb. 16, 2017, in Baku, Azerbaijan.

General Dunford has spoken with General Gerasimov more than a dozen times by phone in the past year or so.

“Both leaders recognize the importance of maintaining regular communication in order to avoid miscalculation and to promote transparency in areas where our militaries are operating in close proximity,” Lt. Cmdr. Hayley Sims, a Dunford spokeswoman, said in an email.

Hotlines and boundaries breached

Nearly three years ago, the Russian and American militaries established a special hotline to help prevent disasters in the air. A United States Air Force officer at Al Udeid Air Base in Qatar calls a Russian officer at an air base in Latakia, Syria, every day to head off — or “deconflict” — potential problems over Syria.

The daily phone calls between the air officers have remained professional. But the dialogue does not always translate into cooperation in the skies.

Last December, Russian fighter jets flew dangerously close to American warplanes in eastern Syria — including one near collision — for about a month. American officials called it a repeated pattern of Russia violating an agreement to keep rival forces separate as they converged on the last main pocket of Islamic State militants in the country.

American and Russian commanders had agreed to fly on opposite sides of a 45-mile stretch of the Euphrates River to prevent accidents in eastern Syria’s increasingly congested skies. But Russian warplanes violated that deal a half-dozen times daily, according to American commanders who said they complained to their counterparts.

In one instance, two Air Force A-10 attack planes flying east of the Euphrates River nearly collided with a Russian Su-24 Fencer just 300 feet away — a close call for jets flying at more than 350 miles per hour. The A-10s swerved to avoid the Russian plane, which was supposed to fly only west of the Euphrates.

Other Russian planes have flown for up to 30 minutes within striking distance or directly over allied ground forces, escalating tensions and risking being shot down, American officials said.

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Russian fighter jets and bombers parked at an air base in Syria.CreditPavel Golovkin/Associated Press

American officers said the violations were an effort by Moscow to test American resolve, bait Air Force pilots into rash reactions and help the Syrian Army seize and control territory ahead of diplomatic talks.

American cruise missile strikes on Syria

Moscow has played small but geopolitically significant roles in the two American cruise missile strikes that in April 2017 targeted an airfield and a year later hit two possible chemical weapons sites and a chemical research lab.

Moscow has been a key ally for Mr. Assad, who has used the Russian military to prop up Syria’s weakened army. In turn, Russia has established a permanent presence at a key airfield and port in western Syria.

In the 2017 strikes, the Pentagon alerted Moscow before 59 Tomahawk cruise missiles hit Al Shayrat Airfield, ensuring that no Russian forces were killed or injured. Moscow said the strikes were couched under a “far-fetched pretext” and had put the Russian military on “the verge of fighting” American troops stationed in Syria’s northeast.

As a result, Russia increased air patrols near American troops in Syria. It also bolstered Syrian air defenses with more advanced surface-to-air missiles. In response, the American Air Force deployed additional advanced-fire aircraft to ensure no Russia forces attacked American ground troops.

Though American military intelligence officials expected blowback from the Russians, Moscow leveled only strong words at the Trump administration. Russian air defenses were not activated as American, French and British aircraft fired salvos of missiles.

“Our warnings have been left unheard,” Russia’s ambassador to the United States, Anatoly Antonov, tweeted after the attacks. “We are being threatened. We warned that such actions will not be left without consequences.”

An attack by Russian mercenaries

On Feb. 7, nearly 500 pro-Syrian government fighters attacked a small American outpost east of the Euphrates River. The American troops there — a mixture of Special Operations forces including Army Rangers and the elite Delta Force — were training and fighting alongside a group of Kurdish fighters called the Syrian Democratic Forces.

American military officials had watched the pro-Syrian government fighters gathering for roughly a week and had intercepted radio transmissions from people speaking Russian among them. Attempting to stave off a potential battle — one that could lead to a wider conflict — officials at the Pentagon alerted their Russian counterparts.

It was to no avail; Moscow denied that the Russian fighters on the ground were connected to Russia’s military.

What ensued was a four-hour firefight that wounded one pro-American Kurdish fighter and killed hundreds of Russians and Syrians. The Pentagon called the incident an act of self-defense. Dozens of American airstrikes forced the pro-Syrian government forces into retreat, leaving the dead on the battlefield and collected later.

While the number of casualties from the firefight is disputed, American intelligence officials have said the Russians were mercenaries who belonged to the shadowy Wagner group, a private military company known for acting on behalf of the Kremlin with little oversight.

The mercenaries loosely coordinate with the Russian military in Syria, and, in the past, have seized oil and gas fields on behalf of Mr. Assad’s government.

Following the battle, the Russian military has started to electronically jam some American aircraft and drones.

Cease-fires in southwestern Syria fall apart

Earlier this month, rebels in southwestern Syria agreed to surrender in a Russian-brokered cease-fire, giving up control of Dara’a Province in another major victory for Mr. Assad and his Russian allies.

State news media reported that the Syrian government seized back the Nassib border crossing with Jordan, which was held by rebels for three years, after an assault in insurgent territory that was backed by Russian airstrikes.

The area had been part of a so-called de-escalation zone, a cease-fire reached last year by Jordan, Russia and the United States to reduce fighting. The Trump administration had warned before the Russian airstrikes that Washington would respond to violations of the agreement.

In the end, however, the administration did nothing, and rebel leaders have said the United States told them to expect no American military help.

A version of this article appears in print on , on Page A11 of the New York edition with the headline: U.S.-Russian Relations in Syria Are Less Rosy Than Leaders Implied. Order Reprints | Today’s Paper | Subscribe